Long time behavior of the solutions to non-linear Kraichnan equations

Alice Guionnet, Christian Mazza

We consider the solution of a nonlinear Kraichnan equation $${\partial }_{s}H(s,t)={\int }_t^{s}H(s,u)H(u,t)k(s,u)du,s\ge t$$ with a covariance kernel $k$ and boundary condition $H…